Pair-density-wave and $s\pm \mathrm{i}d$ superconductivity in a strongly coupled, lightly doped Kondo insulator

We investigate the large Kondo coupling limit of the Kondo-Heisenberg model on one- and two-dimensional lattices. Focusing on the possible superconducting states when slightly doping the Kondo insulator state, we identify different pairing modes to be most stable in different parameter regimes. Possibilities include uniform $s$-wave, pair-density-wave with momentum $\pi$ (in both one and two dimensions) and uniform $s\pm \mathrm{i}d_{x^2-y^2}$-wave (in two dimensions). We attribute these exotic pairing states to the presence of various pair-hopping terms with a ``wrong'' sign in the effective model, a mechanism that is likely universal for inducing pairing states with spatially modulated pair wavefunctions.